Anthony Weiner's Wife Considered Leaving Him, Source Says

Publicly, Huma Abedin said she loves and forgives her husband, Anthony Weiner, despite a second round of sexting revelations.

But a source close to the couple tells PEOPLE she thought of leaving him last fall when Abedin, 36, learned that Weiner, 48, was once again sending sexually explicit messages and photos of himself to other women.

"He came clean to her," says the source, who is a family member.

When he did, Abedin was distraught. "She was seriously considering what to do, thinking: 'Maybe, I can't do this.' There was a possibility of leaving on the table," the source says.

The couple underwent counseling, the source says, and "she made that decision to stay there and see it through for [their son] Jordan's sake and also for Anthony, who she loves very much, and for her sake."

Weiner resigned from Congress in June of 2011 after he admitting to sending messages with sexual content to a number of women.

In July 2012, Weiner told PEOPLE in the first post-scandal interview with the couple: "I've tried to become a better person, a husband that Huma deserves and as good a father as I can be. And I've explored every way to try to do those things and I'm committed to continuing on that path."

Sometime that same month, Weiner began sending sexually explicit messages to a woman named Sydney Leathers, she told Inside Edition. It was about two months later, in September 2012, that Weiner revealed his activities to his wife, the family source tells PEOPLE.

Now running in the Democratic primary for mayor of New York, Weiner hasn't confirmed or denied Leathers's account, saying only some reports are true and some are not. But he admitted to inappropriate online behavior with three women since he left office.